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the Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.
Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1), part II: a semidiscrete error analysis framework for assessing coupling schemes
Abstract. Part I of this study discusses the motivation and empirical evaluation of a revision to the aerosolrelated numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semidiscrete analysis framework for assessing the splitting error of process coupling methods. The framework isolates the error due to numerical splitting from the error from the time integration method(s) used for each individual process. The result is a splitting error expression that is more easily interpreted in the context of the physical processes that the terms represent. The application of this framework to dust life cycle in EAMv1 showcases such an interpretation, using the leadingorder splitting error that results from the framework to confirm (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes, and (ii) that the revised splitting reduces that artificial strengthening.
While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and timestep size for the isolated integration of processes. Such a perspective has the potential for rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.

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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.

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The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.
Journal article(s) based on this preprint
Interactive discussion
Status: closed

RC1: 'Comment on egusphere20231356', Anonymous Referee #1, 02 Sep 2023
Summary
The manuscript presents a novel mathematical framework to investigate the truncation error of splitting methods applied to multiprocess problems. The framework is semidiscrete as it assumes that individual processes are integrated exactly. The framework is demonstrated on two popular coupling algorithms (parallel splitting and sequential splitting). Analytical expressions for the local truncation error (LTE) are rigorously derived both for twoprocess and threeprocess equations. Particularly, it is shown that results derived for twoprocess problems can be used as building blocks to find the expression of the LTE for an arbitrary number of processes. In other words, results can be generalized using logical reasonings, rather than (possibly tedious) mathematical calculations leveraging the Taylor series expansion.
The framework is applied on the dust life cycle modeling of the Energy Exascale Earth System Model version 1 (EAMv1). In the companion paper by Wan et al. (2023), the authors identify three main sources and sinks for dust aerosols in EAMv1: surface emission, dry removal and turbulent mixing. The problem can then be cast as a threeprocess equation. Two splitting algorithms are considered: the original scheme based on sequential splitting, and a revised scheme blending parallel splitting and sequential splitting. The revised coupling scheme leads to a decrease of the magnitude of the leading order term of the LTE associated with dry removal. This is claimed to motivate from a mathematical standpoint the findings of Feng et al. (2022) and Wan et al. (2023).
General comments
The idea of using the Taylor series expansion to calculate the LTE for splitting methods on a template equation is wellestablished. However, compared to similar works available in the literature (properly mentioned in the manuscript), the mathematical apparatus presented here nicely separates the error due to the coupling from the truncation error stemming from the integration of individual processes. I find that the further distinction between isolationinduced and inputinduced errors can provide an intuitive understanding also to modelers who might lack a sound mathematical background. Moreover, the framework is particularly flexible, as it can account for an arbitrary number of processes and it does not make any assumption on the nature of the processes (although some degree of regularity is required to apply fundamental results from calculus).
Nonetheless, I’m a bit skeptical about the direct application of the semidiscrete framework to a fulldiscrete model. Indeed, the assumption that individual processes are integrated exactly is clearly not met in reality, and the overall error introduced by numerical timeintegrators could compensate and/or hide the error associated with the coupling. It follows that even if the framework indicates that the total LTE shrinks when adopting a certain splitting algorithm, the actual model solution might not improve as expected if the splitting error is much smaller than the total error injected by the timeintegrators. Therefore, the semidiscrete framework could fail in providing a comprehensive guidance to the choice of the coupling. I would be curious to read the authors’ opinion on this point.
Regarding the specific case of the dust life cycle modeling in EAMv1, the total LTE for the original and revised coupling is provided in (28) and (32), respectively. The two expressions only differ for the LTE associated with dry removal (process B). By inspection of the sign of A, C and the derivative of B, it is shown that the magnitude of LTE(B) shrinks under the revised coupling method. However, from a pure mathematical perspective, the total LTE cannot be said to decrease in absolute terms without knowing the sign of LTE(A) and LTE(C). I would encourage the authors to provide some insight on the sign of the terms involved in LTE(A) and LTE(C) to better support their claim. Moreover, I would also invite the authors to consider including in the framework the actual timeintegrators used in the model, so as to come up with an estimate of the total LTE that is better tailored to the use case.
Ultimately, I recommend the acceptance of the manuscript, upon addressing the concerns discussed above.
Specific comments
Note: In view of future revisions, the authors may want to consider including line numbers in the manuscript.
 P5, L4: Delete comma after “time”.
 P5, Eq. (2): Readers without a proper mathematical background may wonder where the expression for the propagated error comes from. It might be worth mentioning that this is a wellknown result of calculus.
 P6, L1: Revise typesetting of q_{X_i}. Same comment applies to any following occurrence of this term.
 P9, Eq. (9): Please introduce the abbreviation LTE in Eq. (2).
 P14, Fig. 2, box b2: “y_C^{n+1}” should be “q_C^{n+1}”.
 P15, L15: “the focus here is on the local truncation error”
 P17, right above Eq. (34): “location” should be “local”.
 P19, L23: “The combination of isolationinduced errors leads to an underestimate of the influence of one process on the other.”
 P20, Sect. A1: Could be worth recalling the notation employed in Sect. 2, i.e. that q is a function of time and \phi is the initial condition.
 P23, right above Eq. (A10): “This allows for the simplification of (A8)”.
 P24, right above Eq. (B1): “solving” repeated twice.
Citation: https://doi.org/10.5194/egusphere20231356RC1 
AC1: 'Reply on RC1', Christopher J. Vogl, 30 Oct 2023
We thank the reviewer for their time and effort in reviewing our work, posing some important questions, and catching a number of grammatical mistakes that we missed (and will address in a revision). The comment about line numbers is well taken: we did not realize that EGU would point to our existing preprint on arXiv (which forbids line numbers in submissions) instead of hosting a linenumbered version on their own servers, and we will therefore consider a different preprint server that does allow line numbers for future EGU submissions.
With regard to the reviewer's skepticism about the direct application of the semidiscrete framework to a fulldiscrete model, we agree that LTE caused by splitting is only one contributor to the overall error in a fully discretized system. In situations where the time integration of the individual processes is the dominant source of error, one should not necessarily expect reducing a process splitting LTE to result in an observably more accurate solution. Comprehensive guidance to the choice of the coupling should ideally include consideration of all these factors, and we believe a crucial yet missing piece towards obtaining such a comprehensive guide is an analysis on the errors caused by splitting alone. As such, the manuscript is focused on the splitting error. We note that the dust life cycle problem gives a good example of the role splitting error can play. The earlier studies by Wan et al. (2021, doi: 10.5194/gmd1419212021) and Santos et al. (2021, doi: 10.1029/2020MS002359) showed empirical evidence of process splitting being a major error source in various clouds regimes in EAMv1. In a broader context, the review paper by Gross et al. (2018, MWR, doi: 10.1175/MWRD170345.1) points out that process splitting/coupling has been a largely overlooked topic in the development of weather, climate, and Earth system models.
The framework presented in this manuscript can be extended to include time integration errors from individual processes (by replacing exact integrals with discrete sums reflecting quadratures specific to the process integration methods). Such a more comprehensive analysis can be performed when the time integration methods used in individual processes are sufficiently documented, and we are generally interested in performing such analyses for EAM. When performing the more complete analysis, we imagine that the results about splitting error will be useful building blocks, similar to how the distinction between isolationinduced and inputinduced errors can provide an intuitive understanding of the LTE caused by splitting. We will include some additional discussion on this point in the revised manuscript.
With regard to the reviewer's comment about reducing the total LTE, that comment highlighted the need to better clarify in the revised manuscript that we are not claiming the revised coupling scheme has a smaller total LTE; rather, we intend to claim the revised coupling scheme has a smaller LTE(B). Indeed, reducing the LTE of a single process does not necessarily reduce the total LTE of a coupling scheme, except when that single process is dominating the total LTE. We have seen empirical evidence for both situations in EAMv1 simulations. In the dust life cycle problem, LTE(A) is negligible as emission does not directly depend on aerosol mixing ratio, whereas the sign and magnitude of LTE(C) can vary in time and space. Because EAM is a global model, we generally do not expect to find a simple and robust relationship between LTE(B) and LTE(C) for all grid cells at all times. Therefore, we believe a more reliable approach to reducing the total LTE is to reduce the LTE associated with each and every individual process. This is what we had in mind when saying in the introduction, ``Reducing splitting errors in the process rates can help avoid compensating errors from different physical processes and, thus, help ensure the model provides good predictions of the prognostic variables for the right reasons." Discussions on this point will be expanded in the revised manuscript. We also note that we have some ongoing followup work with the goal of reducing the LTE of all individual terms, which we hope to report on in a separate paper.
With regard to the reviewer's invitation to consider applying the framework to the full process integration, we agree that including the fullydiscrete analysis would very nicely complement the semidiscrete analysis. At this time, a fullydiscrete analysis is difficult due to the limited documentation on the integration approaches used for the individual processes. For this reason, we have elected to focus our manuscript on the semidiscrete results. That said, all the suggestions from the reviewer are well taken. In our view, the two companion papers have made an initial attempt to address one small (albeit important) part of a much larger and complex problem. We are continuing to work towards more complete and comprehensive solutions to the coupling problem, and we hope publishing the results from our initial attempts will invite more researchers in the weather, climate, and Earth system modeling communities to give more attention to the coupling challenge.
Citation: https://doi.org/10.5194/egusphere20231356AC1

RC2: 'Comment on egusphere20231356', Anonymous Referee #2, 15 Sep 2023
This manuscript introduces a mathematical framework for calculating the error associated with two typical time interpolation techniques used in Climate Modeling as well as other multiphysics models. The two techniques in question are sequentialupdatesplitting and parallelsplitting. The manuscript focuses on the error related to aerosol emissions in the E3SM Atmosphere Model v1 (EAMv1) but could be extended to other interphysics coupling with EAM or other similar models. The work presented here provides a valuable tool to climate modelers in a) predicting the numerical error in their models and b) informing decisions about which coupling technique to use. I applaud the authors in doing the work to come up with a mathematical foundation for what is a complicated problem to solve. I recommend this paper for publication in its current form, provided a few minor comments are addressed.
The authors make the argument that this mathematical framework is applicable to other interphysics coupling in models like EAM. This is true, and I think an important result of the research. Could the authors briefly comment on the other factors that go into choosing a coupling technique. For example, cloud macrophysics and microphysics are treated as separate models in EAM but are conceptually tightly coupled. Do the authors have a sense of whether or not this framework would adequately calculate the error between sequential vs. parallel splitting of these processes? A similar question could be asked for the coupling between fluid dynamics and the subgrid physics suite.
1) There is a minor typo in appendix B first sentence "... solving solving ..."
Citation: https://doi.org/10.5194/egusphere20231356RC2 
AC2: 'Reply on RC2', Christopher J. Vogl, 30 Oct 2023
We thank the reviewer for their time and effort in reviewing our work and proving valuable feedback that includes correcting a typo (that we will address in a revision). We are certainly happy to hear the reviewer finds the work a valuable contribution to the climate community.
With regard to the reviewer's request for comment on other factors that go into choosing a coupling technique, we find that multiple factors need to be considered when developing an effective approach to evolving any set of coupled processes together in time. These factors include the time scales of each of the processes, whether the processes together form new time scales, whether the processes depend on each other linearly or nonlinearly, whether one process is highly dependent on another, how accurate the resulting solutions need to be, etc.
Different coupling approaches may try to more frequently evaluate some processes relative to others and thus address tighter dependencies of one process on another. These strategies will give rise to differing error terms which, when instantiated for a given problem, will show differing values.With regard to the reviewer's question about whether the framework would adequately calculate errors for cloud macrophysics and microphysics and/or fluid dynamics and subgrid physics, the mathematical framework presented here provides general expressions for the local truncation errors caused by process splitting. These expressions are generally valid regardless of which physical processes our symbols A and B correspond to. On the other hand, in specific coupling problems like cloud macropyhsics and microphysics or resolved fluid dynamics and parameterized physics, the characteristics of the processes (e.g., the signs, magnitudes, and time scales of A, B, dA/dq, and dB/dq) can differ substantially and also vary significantly in time and space. Therefore, the specific situations may be much more complicated than what we saw in the dust life cycle problem, and the errors of sequential and parallel splitting can be highly dependent on the associated details. Understanding the implications of the error estimates instantiated for a specific situation will continue to require a close collaboration between numerical analysts and climate scientists. Coincidentally, we have done some investigations into coupling problems related to clouds in EAM and plan to report on these in separate papers.
Citation: https://doi.org/10.5194/egusphere20231356AC2

AC2: 'Reply on RC2', Christopher J. Vogl, 30 Oct 2023
Interactive discussion
Status: closed

RC1: 'Comment on egusphere20231356', Anonymous Referee #1, 02 Sep 2023
Summary
The manuscript presents a novel mathematical framework to investigate the truncation error of splitting methods applied to multiprocess problems. The framework is semidiscrete as it assumes that individual processes are integrated exactly. The framework is demonstrated on two popular coupling algorithms (parallel splitting and sequential splitting). Analytical expressions for the local truncation error (LTE) are rigorously derived both for twoprocess and threeprocess equations. Particularly, it is shown that results derived for twoprocess problems can be used as building blocks to find the expression of the LTE for an arbitrary number of processes. In other words, results can be generalized using logical reasonings, rather than (possibly tedious) mathematical calculations leveraging the Taylor series expansion.
The framework is applied on the dust life cycle modeling of the Energy Exascale Earth System Model version 1 (EAMv1). In the companion paper by Wan et al. (2023), the authors identify three main sources and sinks for dust aerosols in EAMv1: surface emission, dry removal and turbulent mixing. The problem can then be cast as a threeprocess equation. Two splitting algorithms are considered: the original scheme based on sequential splitting, and a revised scheme blending parallel splitting and sequential splitting. The revised coupling scheme leads to a decrease of the magnitude of the leading order term of the LTE associated with dry removal. This is claimed to motivate from a mathematical standpoint the findings of Feng et al. (2022) and Wan et al. (2023).
General comments
The idea of using the Taylor series expansion to calculate the LTE for splitting methods on a template equation is wellestablished. However, compared to similar works available in the literature (properly mentioned in the manuscript), the mathematical apparatus presented here nicely separates the error due to the coupling from the truncation error stemming from the integration of individual processes. I find that the further distinction between isolationinduced and inputinduced errors can provide an intuitive understanding also to modelers who might lack a sound mathematical background. Moreover, the framework is particularly flexible, as it can account for an arbitrary number of processes and it does not make any assumption on the nature of the processes (although some degree of regularity is required to apply fundamental results from calculus).
Nonetheless, I’m a bit skeptical about the direct application of the semidiscrete framework to a fulldiscrete model. Indeed, the assumption that individual processes are integrated exactly is clearly not met in reality, and the overall error introduced by numerical timeintegrators could compensate and/or hide the error associated with the coupling. It follows that even if the framework indicates that the total LTE shrinks when adopting a certain splitting algorithm, the actual model solution might not improve as expected if the splitting error is much smaller than the total error injected by the timeintegrators. Therefore, the semidiscrete framework could fail in providing a comprehensive guidance to the choice of the coupling. I would be curious to read the authors’ opinion on this point.
Regarding the specific case of the dust life cycle modeling in EAMv1, the total LTE for the original and revised coupling is provided in (28) and (32), respectively. The two expressions only differ for the LTE associated with dry removal (process B). By inspection of the sign of A, C and the derivative of B, it is shown that the magnitude of LTE(B) shrinks under the revised coupling method. However, from a pure mathematical perspective, the total LTE cannot be said to decrease in absolute terms without knowing the sign of LTE(A) and LTE(C). I would encourage the authors to provide some insight on the sign of the terms involved in LTE(A) and LTE(C) to better support their claim. Moreover, I would also invite the authors to consider including in the framework the actual timeintegrators used in the model, so as to come up with an estimate of the total LTE that is better tailored to the use case.
Ultimately, I recommend the acceptance of the manuscript, upon addressing the concerns discussed above.
Specific comments
Note: In view of future revisions, the authors may want to consider including line numbers in the manuscript.
 P5, L4: Delete comma after “time”.
 P5, Eq. (2): Readers without a proper mathematical background may wonder where the expression for the propagated error comes from. It might be worth mentioning that this is a wellknown result of calculus.
 P6, L1: Revise typesetting of q_{X_i}. Same comment applies to any following occurrence of this term.
 P9, Eq. (9): Please introduce the abbreviation LTE in Eq. (2).
 P14, Fig. 2, box b2: “y_C^{n+1}” should be “q_C^{n+1}”.
 P15, L15: “the focus here is on the local truncation error”
 P17, right above Eq. (34): “location” should be “local”.
 P19, L23: “The combination of isolationinduced errors leads to an underestimate of the influence of one process on the other.”
 P20, Sect. A1: Could be worth recalling the notation employed in Sect. 2, i.e. that q is a function of time and \phi is the initial condition.
 P23, right above Eq. (A10): “This allows for the simplification of (A8)”.
 P24, right above Eq. (B1): “solving” repeated twice.
Citation: https://doi.org/10.5194/egusphere20231356RC1 
AC1: 'Reply on RC1', Christopher J. Vogl, 30 Oct 2023
We thank the reviewer for their time and effort in reviewing our work, posing some important questions, and catching a number of grammatical mistakes that we missed (and will address in a revision). The comment about line numbers is well taken: we did not realize that EGU would point to our existing preprint on arXiv (which forbids line numbers in submissions) instead of hosting a linenumbered version on their own servers, and we will therefore consider a different preprint server that does allow line numbers for future EGU submissions.
With regard to the reviewer's skepticism about the direct application of the semidiscrete framework to a fulldiscrete model, we agree that LTE caused by splitting is only one contributor to the overall error in a fully discretized system. In situations where the time integration of the individual processes is the dominant source of error, one should not necessarily expect reducing a process splitting LTE to result in an observably more accurate solution. Comprehensive guidance to the choice of the coupling should ideally include consideration of all these factors, and we believe a crucial yet missing piece towards obtaining such a comprehensive guide is an analysis on the errors caused by splitting alone. As such, the manuscript is focused on the splitting error. We note that the dust life cycle problem gives a good example of the role splitting error can play. The earlier studies by Wan et al. (2021, doi: 10.5194/gmd1419212021) and Santos et al. (2021, doi: 10.1029/2020MS002359) showed empirical evidence of process splitting being a major error source in various clouds regimes in EAMv1. In a broader context, the review paper by Gross et al. (2018, MWR, doi: 10.1175/MWRD170345.1) points out that process splitting/coupling has been a largely overlooked topic in the development of weather, climate, and Earth system models.
The framework presented in this manuscript can be extended to include time integration errors from individual processes (by replacing exact integrals with discrete sums reflecting quadratures specific to the process integration methods). Such a more comprehensive analysis can be performed when the time integration methods used in individual processes are sufficiently documented, and we are generally interested in performing such analyses for EAM. When performing the more complete analysis, we imagine that the results about splitting error will be useful building blocks, similar to how the distinction between isolationinduced and inputinduced errors can provide an intuitive understanding of the LTE caused by splitting. We will include some additional discussion on this point in the revised manuscript.
With regard to the reviewer's comment about reducing the total LTE, that comment highlighted the need to better clarify in the revised manuscript that we are not claiming the revised coupling scheme has a smaller total LTE; rather, we intend to claim the revised coupling scheme has a smaller LTE(B). Indeed, reducing the LTE of a single process does not necessarily reduce the total LTE of a coupling scheme, except when that single process is dominating the total LTE. We have seen empirical evidence for both situations in EAMv1 simulations. In the dust life cycle problem, LTE(A) is negligible as emission does not directly depend on aerosol mixing ratio, whereas the sign and magnitude of LTE(C) can vary in time and space. Because EAM is a global model, we generally do not expect to find a simple and robust relationship between LTE(B) and LTE(C) for all grid cells at all times. Therefore, we believe a more reliable approach to reducing the total LTE is to reduce the LTE associated with each and every individual process. This is what we had in mind when saying in the introduction, ``Reducing splitting errors in the process rates can help avoid compensating errors from different physical processes and, thus, help ensure the model provides good predictions of the prognostic variables for the right reasons." Discussions on this point will be expanded in the revised manuscript. We also note that we have some ongoing followup work with the goal of reducing the LTE of all individual terms, which we hope to report on in a separate paper.
With regard to the reviewer's invitation to consider applying the framework to the full process integration, we agree that including the fullydiscrete analysis would very nicely complement the semidiscrete analysis. At this time, a fullydiscrete analysis is difficult due to the limited documentation on the integration approaches used for the individual processes. For this reason, we have elected to focus our manuscript on the semidiscrete results. That said, all the suggestions from the reviewer are well taken. In our view, the two companion papers have made an initial attempt to address one small (albeit important) part of a much larger and complex problem. We are continuing to work towards more complete and comprehensive solutions to the coupling problem, and we hope publishing the results from our initial attempts will invite more researchers in the weather, climate, and Earth system modeling communities to give more attention to the coupling challenge.
Citation: https://doi.org/10.5194/egusphere20231356AC1

RC2: 'Comment on egusphere20231356', Anonymous Referee #2, 15 Sep 2023
This manuscript introduces a mathematical framework for calculating the error associated with two typical time interpolation techniques used in Climate Modeling as well as other multiphysics models. The two techniques in question are sequentialupdatesplitting and parallelsplitting. The manuscript focuses on the error related to aerosol emissions in the E3SM Atmosphere Model v1 (EAMv1) but could be extended to other interphysics coupling with EAM or other similar models. The work presented here provides a valuable tool to climate modelers in a) predicting the numerical error in their models and b) informing decisions about which coupling technique to use. I applaud the authors in doing the work to come up with a mathematical foundation for what is a complicated problem to solve. I recommend this paper for publication in its current form, provided a few minor comments are addressed.
The authors make the argument that this mathematical framework is applicable to other interphysics coupling in models like EAM. This is true, and I think an important result of the research. Could the authors briefly comment on the other factors that go into choosing a coupling technique. For example, cloud macrophysics and microphysics are treated as separate models in EAM but are conceptually tightly coupled. Do the authors have a sense of whether or not this framework would adequately calculate the error between sequential vs. parallel splitting of these processes? A similar question could be asked for the coupling between fluid dynamics and the subgrid physics suite.
1) There is a minor typo in appendix B first sentence "... solving solving ..."
Citation: https://doi.org/10.5194/egusphere20231356RC2 
AC2: 'Reply on RC2', Christopher J. Vogl, 30 Oct 2023
We thank the reviewer for their time and effort in reviewing our work and proving valuable feedback that includes correcting a typo (that we will address in a revision). We are certainly happy to hear the reviewer finds the work a valuable contribution to the climate community.
With regard to the reviewer's request for comment on other factors that go into choosing a coupling technique, we find that multiple factors need to be considered when developing an effective approach to evolving any set of coupled processes together in time. These factors include the time scales of each of the processes, whether the processes together form new time scales, whether the processes depend on each other linearly or nonlinearly, whether one process is highly dependent on another, how accurate the resulting solutions need to be, etc.
Different coupling approaches may try to more frequently evaluate some processes relative to others and thus address tighter dependencies of one process on another. These strategies will give rise to differing error terms which, when instantiated for a given problem, will show differing values.With regard to the reviewer's question about whether the framework would adequately calculate errors for cloud macrophysics and microphysics and/or fluid dynamics and subgrid physics, the mathematical framework presented here provides general expressions for the local truncation errors caused by process splitting. These expressions are generally valid regardless of which physical processes our symbols A and B correspond to. On the other hand, in specific coupling problems like cloud macropyhsics and microphysics or resolved fluid dynamics and parameterized physics, the characteristics of the processes (e.g., the signs, magnitudes, and time scales of A, B, dA/dq, and dB/dq) can differ substantially and also vary significantly in time and space. Therefore, the specific situations may be much more complicated than what we saw in the dust life cycle problem, and the errors of sequential and parallel splitting can be highly dependent on the associated details. Understanding the implications of the error estimates instantiated for a specific situation will continue to require a close collaboration between numerical analysts and climate scientists. Coincidentally, we have done some investigations into coupling problems related to clouds in EAM and plan to report on these in separate papers.
Citation: https://doi.org/10.5194/egusphere20231356AC2

AC2: 'Reply on RC2', Christopher J. Vogl, 30 Oct 2023
Peer review completion
Journal article(s) based on this preprint
Data sets
EAMv1 output from simulations using tag v1_cflx_2021: annual averages Hui Wan, Kai Zhang https://doi.org/10.5281/zenodo.7996742
EAMv1 output from simulations using tag v1_cflx_2021: instantaneous values Hui Wan, Kai Zhang https://doi.org/10.5281/zenodo.8000745
Model code and software
EAMv1 code with revised aerosol process coupling (tag v1_cflx_2021) Hui Wan https://doi.org/10.5281/zenodo.7995850
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Carol S. Woodward
Quan M. Bui
The requested preprint has a corresponding peerreviewed final revised paper. You are encouraged to refer to the final revised version.